Question

Find x :
under root (x+1) - under root (x-1) = under root (4x-1)​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

How many solutions does the equation under root (x+1)-under root (x-1)=under root (4x-1) have?

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Root(x+1)-root(x-1) = rt(4x-1)

Squaring both sides, (x+1)-2 rt(x+1)(x-1) +x-1 = 4x-1

2x - 2rt(x^2–1) = 4x-1

-2rt(x^2–1) = 2x-1

Squaring again, 4(x^2–1) = (2x-1)^2

4x^2 - 4 = 4x^2 - 4x +1

4x=5. So, x=5/4

So there is only one root for the given equation.

Care: When we substitute 5/4 in the equation, we have to negative square root for the first root, positive square root for the second on the LHS of the equation and negative square root of the RHS.

-3/2 -1/2 =-2.

Other signs of the roots do not satisfy the given equation.

Step-by-step explanation:

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